APPENDIX A

Literature Review

A.1 Load Rating State-of-the-Art Review (AASHTO MBE)

Table A-1 contains insights and MBE articles on provisions for segmental bridges.

Table A-1. AASHTO MBE provisions regarding segmental bridges.

A.2 Calibration of LRFD Concrete Design Service

Cracking of Reinforced Concrete Components Service I Limit State

The original service limit state from AASHTO’s Standard Specifications for Highway Bridges (AASHTO 2002) is to limit the concrete crack width, and there was no evidence to change these evaluation criteria. As a result, the study was based on keeping the present crack width data and calibrating the limit state to provide a uniform reliability index that was similar to the current average reliability index. The crack width is limited to 0.017 in. and 0.01275 in. for Class 1 and Class 2 exposure conditions, respectively.

To evaluate the safety level of the current LRFD, a set of bridge decks with varied girder spacings and deck thicknesses were designed using the AASHTO LRFD (2020a). The statistical parameters of variables included in the design were largely adopted from previous research (Naaman and Siriaksorn 1982; Nowak et al. 2008). In this study, the live load statistics were derived in terms of the axle weights. Extrapolations were performed for different ADTT and different return periods.

The concrete deck can be controlled by either strength limit state or Service I limit state. The Service I limit state is frequently controlling the negative moment region. As a result, the reliability indices for the negative moment region are thought to be typical of the real reliability indices that would be determined if all limit states, including Strength I, were considered in the design. The target reliability indices were chosen to be 1.6 and 1.0 for Class 1 and Class 2, respectively, based on the ADTT of 5,000.

The Monte Carlo simulation was used to generate thousands of iterations of each variable, and the final reliability index was calculated using Eq. (6-27), where β is reliability index, µ_R is the mean value of the resistance, µ_Q is the mean value of the applied loads, σ_R is the standard deviation of the resistance, and σ_Q is the standard deviation of the applied load. As the current LRFD specification produces uniform reliability indices around the target value, this study does not necessitate any revisions to the AASHTO LRFD related to the crack control limit state (i.e., Service I limit state).

Tension in Prestressed Concrete Beam Service III Limit State

The following three limit state functions were investigated:

• Decompression limit state: This limit state assumes that failure occurs when the stress in the concrete on the tension face computed based on the uncracked portion ceases to be compression due to the combined influence of factored dead load and live load.
• Stress limit state: This limit state assumes that failure occurs when the tensile stress in the concrete on the tension face calculated based on the uncracked section exceeds a certain tensile stress limit calculated based on the uncracked section properties under the combined effect of factored dead load and live load, regardless of whether the section has been previously cracked.
• Crack width limit state: This limit state assumes that failure occurs when a previously established crack in the concrete opens and reaches a pre-specified crack width.

To evaluate the safety level of the existing prestressed concrete element, the study referred to a database of existing prestressed concrete girder bridges from NCHRP Report 700: A Comparison of AASHTO Bridge Load Rating Methods (Mlynarski et al. 2011). The statistical parameters of variables included in the design were adopted from previous research (Gross 2000; Naaman and Siriaksorn 1982; Nowak et al. 2008; Tadros et al. 2003). The live load statistics were derived in terms of the live load moment on the girder. The bias factor is calculated by using the mean maximum load effect ratio increased by a 1.5 standard deviation to account for the loss of randomness of the WIM site selections.

Based on the existing bridge database, the study compared the required load and the corresponding reliability index for each limit state, as shown in Table A-2.

In addition to the existing bridge database, the study also designed for a series of new bridges in accordance with the two maximum concrete tensile stress limits. Various span lengths and girder spacings are enveloped by the database. These bridges were redesigned six times taking into account the following parameters:

1. Live load factor = 0.8 or 1.0.
2. Tensile strength limit $f_t=0.0948\sqrt{f_c^{\prime }}\text{or}0.19\sqrt{f_c^{\prime }}\text{or}0.25\sqrt{f_c^{\prime }}$.

The same methodology deployed by the Service I limit state was used here to compute the reliability indices. The reliability indices were computed for each design case. Despite the maximum tensile stress limit used in the design, the maximum tensile stress limiting criteria for calculating the reliability index was set at $f_t=0.19\sqrt{f_c^{\prime }}$ in ksi.

In all, the reliability indices revealed the following conclusions:

• The maximum level of uniformity was found in the decompression limit state, which is recommended to be used as the basis for the reliability analysis.
• The reliability indices are not sensitive to ADTT.
• The target reliability index is chosen to be similar to the average inherent reliability index of the existing bridges due to their satisfactory performance.
• It is recommended to use a live load factor of 1.0 for Service III limit state. The concrete tensile stress of $0.0948\sqrt{f_c^{\prime }}$ and $0.19\sqrt{f_c^{\prime }}$ are recommended for bridges in severe corrosion conditions and for bridges in moderate corrosion conditions, respectively.

A.3 Deterioration of Segmental Bridges

Segmental and post-tensioned bridges most likely have high structural performance. Deterioration for such bridges have been mostly related to the corrosion of tendons, cracks due to temperature gradients, or early age failure of tendons (Roberts 1993; Trejo et al. 2009). Material-wise, it is known that concrete deterioration due to environmental conditions or time-dependent material behavior, such as creep, shrinkage, and relaxation, are widely seen in concrete bridges. Based on the response of the Wisconsin DOT to a questionnaire conducted to reveal common deterioration issues and repair techniques, concrete deterioration was reported as the major problem. Based on the survey, the top five types of concrete deterioration are cracking, delamination, spalling, rebar corrosion, and scaling (Ainge 2012). Furthermore, Virmani (2003)

The effect of strand corrosion on structural behavior has been investigated by researchers through experimental testing and analytical models. Zhang et al. (2017) evaluated the behavior of locally ungrouted post-tensioned concrete beams after corrosion of strands by performing corroded strand tests for the constitutive law development and beam tests for the flexural behavior investigation. It was observed that the effect of corrosion loss on the yield strength and elastic modulus was less than that on the ultimate strain of strand. Salas et al. (2008) investigated the corrosion protection of internal tendons at segmental joints by using the testing method based on ASTM G109. They fabricated beam specimens to observe effects of post-tensioning and crack width on corrosion protection of internal tendons. The experimental setup is given in Figure A-1. In general, severe duct destruction and pitting were observed in most of the specimens with metal ducts. Haixue and Whitmore (2013) listed the methods in post-tensioning evaluation as visual inspection/test pits, PT corrosion evaluation by moisture testing, chloride analysis of PT grout, pH and chemical testing, petrographic analysis, scanning electron microscopy examination, and cable break detection.

Hatami et al. (2011) developed deterioration models for the three main bridge components (deck, superstructure, substructure) of Nebraska bridges by considering deterioration factors, such as the impact of structure type, deck type, wearing surface, deck protection, ADT, ADTT, and highway district, using visual inspection data from 1998 to 2010. Moomen et al. (2016) developed deterministic and probabilistic deterioration models (or curves) for bridge decks, superstructures, and substructures using the NBI database to support Indiana’s Bridge Management System. The climate variables of freeze index, number of freeze-thaw cycles, and average precipitation were found to be significant parameters for several deterioration models, and for deck and substructure especially. Purvis et al. (1992) developed various performance and deterioration models representing a numerical simulation of data collected on populations of bridges using NBI numerical condition ratings. However, it has been stated that because NBI condition ratings are generally based on a visual inspection, they would not detect a corrosion problem until significant concrete spalling could be seen. Naderimoghaddam (2018) stated that deterioration models are currently presented for a specific bridge component but not for the sufficiency rating. He introduced two models—the mixed logistics-gamma model and the Poisson model—to predict the change in the sufficiency rating of a bridge. The former one was found to be a better model.

The corrosion progress of steel wires in external tendons contaminated by water with high chloride content from the outside of a bridge was modeled by Yoo et al. (2018). Existing corrosion-progress models and proposed models were compared. In one of the existing corrosion-progress methods, the corrosion model for rebars introduced by Val and Melchers (1997) was modified to simulate pitting corrosion in wires since the shape of rebars and wires are similar (Darmawan and Stewart 2007; Guo et al. 2011). The model assumed that pits have a hemispherical form fixing at the top, and that corrosion progresses radially. In this model, the corroded area (A_SL,1) can be calculated by using the maximum corrosion depth (p) as follows:

$\begin{array}{cc}{A}_{\text{SL},1}=r^2\left(\text{θ}-\text{sin}{\text{θ}}_1-\text{cos}{\text{θ}}_1\right)+p^2\left({\text{θ}}_2-\text{sin}{\text{θ}}_2-\text{cos}{\text{θ}}_1\right)& \text{for}0\end{array}\le {\text{θ}}_1\le \text{π}$

where r = radius of wire, p = maximum corrosion depth, and θ₁ and θ₂ = functions of p defined as:

${\text{θ}}_1=\text{arccos}\left(1-\frac{p^2}{2r^2}\right)$

${\text{θ}}_2=\text{arccos}\left(\frac{p^2}{2r}\right)$

In another corrosion model developed by Hartt and Lee (2016), it was assumed that corrosion progresses in a planar shape, and the shape of the corroded area is diffused over the entire surface of the wire. The corroded area (A_SL,2) can be defined in terms of p as follows:

$\begin{array}{cc}{A}_{\text{SL},2}=r^2\left(\text{θ}-\text{sin}{\text{θ}}_1-\text{cos}{\text{θ}}_1\right)& \text{for}0\end{array}\le {\text{θ}}_1\le \text{π}$

where r = radius of wire and θ₁ = function of p defined as follows:

${\text{θ}}_1=\text{arccos}\left(1-\frac{p}{r}\right)$

The model proposed by Yoo et al. (2018) provided a better estimate of section loss corresponding to the maximum corrosion depth. It assumed a rounded corrosion surface with the center fixed at the perimeter of the wire. The corroded area (A_SL,3) can be defined in terms of p as follows.

$\begin{array}{cc}{A}_{\text{SL},3}=r^2\left(\text{θ}-\text{sin}{\text{θ}}_1-\text{cos}{\text{θ}}_1\right)+s^2\left({\text{θ}}_2-\text{sin}{\text{θ}}_2-\text{cos}{\text{θ}}_1\right)& \text{for}0\end{array}\le {\text{θ}}_1\le \text{π}$

where s = 2r-p and θ₁ and θ₂ = functions of s and r defined as:

${\text{θ}}_1=2{\text{θ}}_2$

${\text{θ}}_2=\text{arccos}\left(\frac{s}{2r}\right)$

Since reaching the maximum corrosion depth requires a large number of measurements, measuring the corrosion perimeter by inserting an endoscope or a borescope into the tendon might be an alternative (Yoo et al. 2018). Another model, identical to the first proposed model but which has different definitions for θ₁, θ₂, and s was proposed considering the relationship between the corrosion perimeter and the maximum corrosion depth as follows. It was shown

$\begin{array}{cc}{A}_{\text{SL},3}=r^2\left({\text{θ}}_3-\text{sin}{\text{θ}}_3-\text{cos}{\text{θ}}_3\right)& \text{for}0\end{array}\le d_p\le 2r$

${\text{θ}}_3=\text{arccos}\left(1-\frac{d_p}{r}\right)$

Where A_SL,_1–3 is the loss of sectional area according to the type of pit configuration, r is the radius of a wire, and d_p is the pit depth measured by depth gauge at the deepest location.

Trejo et al. (2009) performed a 1-year-long strand corrosion test program to identify and quantify the factors affecting corrosion and tendon capacity of PT strands. The authors considered grout class, moisture content, chloride concentration, void type, and stress level. The results showed that the most severe corrosion existed at or near the grout-air-strand interface. Also, orthogonal, inclined, and bleedwater void conditions were more corrosive than parallel and no-void conditions. Salas et al. (2002) conducted research related to corrosion protection for bonded internal tendons in precast segmental construction. The researchers evaluated the effect of different parameters such as joint type, duct type, joint precompression, and grout type. Based on the experimental results, it was seen that the most significant effect is the joint type. The highest strand corrosion ratings, thus, the largest deterioration, were observed on dry joint specimens with normal grout and low-to-medium precompression. The epoxy joint specimen with the same grout type, duct, and precompression force had strand corrosion ratings on the order of 8 to 10 times smaller. Also, steel ducts showed a much higher corrosion rating than plastic ducts. The effect of grout type on strand corrosion is given in Figure A-2. Jeon et al. (2019) investigated corrosion of external tendons of two segmental bridges located on an urban arterial road. The location of the corrosion was mostly inside the duct, having voids not filled by the grout. Rafols et al. (2013) exemplify areas of anticipated corrosion susceptibility as the tendon high points, grout void locations, and other locations with grout deficiencies.

Corrosion Rate versus Time

Lee and Zielske (2014) conducted a 6-month accelerated corrosion testing program to determine chloride threshold(s) of post-tensioning strands exposed to chloride-contaminated grout. Chloride threshold values of 0.4% and 0.8% by weight of cement were obtained for corrosion initiation and corrosion propagation, respectively. It was seen that the corrosion rate with time for the single wires in pH 13.6 solutions was lower than 0.05 mil/year at chloride concentrations up to 0.6%. In another study conducted by FHWA, the relation of time to initial fracture/failure and mean corrosion rate is obtained from the experimental grout study of four standard deviation of corrosion rate/mean corrosion rate ratios [σ(CRE)/µ(CRE)] (see Figure A-3) (Hartt and Lee 2016). Mean and standard deviation of corrosion rates are given as the function of chloride concentration in physically sound grout, and time to failure (T_f) is given as the function of mean corrosion rate for four different σ(CRE)/µ(CRE) ratios.

A.4 Condition Factors

Resistance Statistical Parameters

The original calibration work for the load rating condition factor was done in NCHRP Project 12-28. The statistical parameters consist of a bias factor and a coefficient of variation (V), accounting for the uncertainties caused by material yield, fabrication, and accuracy of strength

Table A-6. Illustrative examples for φ_c.

The FDOT (2002) conducted a study to recommend some improvements in the load rating of post-tensioned concrete segmental bridges. For the bridges built in accordance with the FDOT’s New Directions for Florida Post-Tensioned Bridges, a 1.10 condition factor might be used. The same study also presents illustrative examples for φ_c, as can be seen in Table A-6. It is proposed that the low value (0.85) might be applied to local corroded cross section(s) and a higher value to other satisfactory areas.